Question

Antimony ( \[Sb\] ) is \[57.2\% \] \[Sb - 121\] and \[42.8\% \]\[Sb - 123\] . Calculate the average atomic mass?
A. \[121.6\]
B. \[121.8\]
C. \[122.4\]
D. \[121.9\]

Answer 1

Hint:In order to find the answer we need to first convert the percentages into fractions by dividing them by \[100\] . Then we will calculate the average mass using the average atomic mass formula for isotopes. Average atomic mass \[ = {{ }}{f_1}{M_1}\; + {{ }}{f_2}{M_2}\; + \ldots {{ }} + {{ }}{f_n}{M_n}\]
Formula used: Average atomic mass \[ = {{ }}{f_1}{M_1}\; + {{ }}{f_2}{M_2}\; + \ldots {{ }} + {{ }}{f_n}{M_n}\]
Where, \[f\] is called the fraction which represents the natural abundance of that particular isotope; and \[M\] is the mass number (or the weight) of the given isotope.
Complete step by step answer:
The average atomic mass of an element is calculated by doing the sum of the masses of all its isotopes, each is multiplied by its natural abundance (the decimal which is associated with percent of the atoms of that element that are of that particular given isotope).
Converting percentages to fractions, we have ${f_1} = \dfrac{57.2}{100}= 0.572$
And second fraction would be ${f_2} = \dfrac{42.8}{100} = 0.428$
Mass numbers are ${M_1} = 121$ and ${M_2} = 123$
By putting the values in the equation, we have
Average atomic mass $ = (0.572 \times 121) + (0.428 \times 123)$
$ = 69.212 + 52.644$
On adding we get $121.856$ ( $ \sim 121.9$ ) and the unit will be $gm/mol$ .
Therefore the answer is Option D.

Additional Information: Atoms of the same element are known to have differing numbers of neutrons in their nucleus. For instance, stable helium atoms exist which contain either one or two neutrons, but both the atoms have two protons. These different types of helium atoms have different masses (3 or 4 atomic mass units), and they are called isotopes. For any given isotope, the sum of the numbers of protons and neutrons in the nucleus is called the mass number.

Note:
-If in place of mass number, number of protons and neutrons are given, the sum of the two will give the value of mass number.
-Also, it is important to note that the number of electrons is equal to the number of protons in a neutral atom .